Consider the family of non-intersecting, hexagonal (\(N=6\)) orbits in an elliptic billiard, \(a/b=1.5\). Each hexagon contains three distinct subtriangles (up to cyclic symmetry), e.g., defined by vertices 123, 124 and 135:

Each row below depicts the locus of \(X(i)\), \(i=1,2,\ldots 100\) for those subtriangles shown combined and separately.

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